Solution diffusion model sorption process

Good quality RO membranes can reject >95-99% of the NaCl from aqueous feed streams (Baker, Cussler, Eykamp et al., 1991 Scott, 1981). The morphologies of these membranes are typically asymmetric with a thin highly selective polymer layer on top of an open support structure. Two rather different approaches have been used to describe the transport processes in such membranes the solution-diffusion (Merten, 1966) and surface force capillary flow model (Matsuura and Sourirajan, 1981). In the solution-diffusion model, the solute moves within the essentially homogeneously solvent swollen polymer matrix. The solute has a mobility that is dependent upon the free volume of the solvent, solute, and polymer. In the capillary pore diffusion model, it is assumed that separation occurs due to surface and fluid transport phenomena within an actual nanopore. The pore surface is seen as promoting preferential sorption of the solvent and repulsion of the solutes. The model envisions a more or less pure solvent layer on the pore walls that is forced through the membrane capillary pores under pressure. 

Usually the mathematical description of the process is expressed by a solution-diffusion model, which could take into account some non-linear phenomena for both the sorption and the diffusion steps. Anomalous behaviours are frequently observed and are typical for polymers, which very often constitute the material of the selective layer of the membrane. Swelling, which accompanies the sorption of chemicals into polymers, is just one of the most important non-linear phenomena. Due to the presence of the per-meants in the membrane, swelling is not uniform and produces non-linear gradients of permeant concentration inside the membrane. 

The process of permeation through non-porous polymers is generally explained in terms of the solution diffusion model. This model postulates that the permeation of a gas through a polymer film occurs in three stages (1) sorption of the gas on to the polymer, (2) diffusion through the polymer and (3) desorption from the opposite face. Thus it can be seen that the permeability P is given by a combination of the diffusivity of the gas D dissolved in the polymer and its concentration gradient, which in turn is proportional to the gas solubility S in the polymer. 

The kinetics of sorption can be considered as the sum of two processes 1) rapid sorption by labile sites which are in equilibrium with solutes dissolved in bulk solution, and 2) hindered sorption by sites which are accessible only by slow diffusion. Alternatively, sorption kinetics can be modeled by a radial diffu-sional process into spherical sorbents. The slow sorption process prevents complete equilibration within one day, the time used in typical batch experiments. Because the apparent rate of diffusion decreases with increasing hydrophobicity, time to equilibrium is longer for highly hydrophobic compounds. 

Selective separation of hquids by pervaporation is a result of selective sorption and diffusion of a component through the membrane. PV process differs from other membrane processes in the fact that there is a phase change of the permeating molecules on the downstream face of the membrane. PV mechanism can be described by the solution-diffusion mechanism proposed by Binning et al. [3]. According to this model, selective sorption of the component of a hquid mixture takes place at the upstream face of the membrane followed by diffusion through the membrane and desorption on the permeate side. 

One aspect of the model is the assumption of constant Knudsen diffusivity. To validate this assumption, we can extract the diffusivity from the short time solution as it reflects the transient behaviour of the system, and also extract the diffusivity from the time lag information. The latter reflects the overall kinetic behaviour of the system. If the two extracted diffiisivities are the same then the assumption of constant diffusivity holds and the system is a pure diffusion system. On the other hand, if the diffusion coefficient extracted from the short time solution is smaller than the steady state diffusivity, then there exists a sorption process occuring during the transient operation within the medium as the steady state flow is unaffected by the amount adsorbed. 

This article focuses on transport that proceeds by the solution-diffusion mechanism. Transport by this mechanism requires that the penetrant sorb into the polymer at a high activity interface, diffuse through the poljuner, and then desorb at a low activity interface. In contrast, the pore-flow mechanism transports penetrants hy convective flow through porous pol5uners and will not be described in this article. Detailed models exist for the solution and diffusion processes of the solution-diffusion mechanism. The differences in the sorption and transport properties of rubbery and glassy pol5uners are reviewed and discussed in terms of the fundamental differences between the intrinsic characteristics of these two types of polymers. 

The moments of the solutions thus obtained are then related to the individual mass transport diffusion mechanisms, dispersion mechanisms and the capacity of the adsorbent. The equation that results from this process is the model widely referred to as the three resistance model. It is written specifically for a gas phase driving force. Haynes and Sarma included axial diffusion, hence they were solving the equivalent of Eq. (9.10) with an axial diffusion term. Their results cast in the consistent nomenclature of Ruthven first for the actual coefficient responsible for sorption kinetics as ... 

The kinetic properties of strontium sorption on clinoptilolite from both model solutions and natural seawater have been investigated in detail [252, 253]. These properties are determined by diffusion in both the zeolite microcrystals and the intercrystalline porous space [252]. Methods for determining the characteristic size of microcrystals by an ion-exchange technique are given in [253]. Such estimates provided a determination of their size-based contribution to the diffusion process. 

Fundamentals of sorption and sorption kinetics by zeohtes are described and analyzed in the first Chapter which was written by D. M. Ruthven. It includes the treatment of the sorption equilibrium in microporous sohds as described by basic laws as well as the discussion of appropriate models such as the Ideal Langmuir Model for mono- and multi-component systems, the Dual-Site Langmuir Model, the Unilan and Toth Model, and the Simphfied Statistical Model. Similarly, the Gibbs Adsorption Isotherm, the Dubinin-Polanyi Theory, and the Ideal Adsorbed Solution Theory are discussed. With respect to sorption kinetics, the cases of self-diffusion and transport diffusion are discriminated, their relationship is analyzed and, in this context, the Maxwell-Stefan Model discussed. Finally, basic aspects of measurements of micropore diffusion both under equilibrium and non-equilibrium conditions are elucidated. The important role of micropore diffusion in separation and catalytic processes is illustrated. 

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